On the eigenvalues for slowly varying perturbations of a periodic Schrödinger operator

Details On the eigenvalues for slowly varying perturbations of a periodic Schrödinger operator On the eigenvalues for slowly varying perturbations of a periodic Schrödinger operator

2005-03-12

arxiv.org/abs/math-ph/0503031v1

Physics

Mathematical Physics

soumis en d\'{e}cembre 2004

Scientific paper

In this paper, I consider one-dimensional periodic Schr{\"o}dinger operators perturbed by a slowly decaying potential. In the adiabatic limit, I give an asymptotic expansion of the eigenvalues in the gaps of the periodic operator. When one slides the perturbation along the periodic potential, these eigenvalues oscillate. I compute the exponentially small amplitude of the oscillations.

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